Can I use MatterControl to run G-Code generated by another slicer?

Yes, you can use G-Code files with MatterControl even if they are generated by another program. 

To do so, you'd just add the .gcode file to the QUEUE like any other model. You won't see a 3D model in 3D VIEW, but LAYER VIEW should show the print as it will print layer by layer so long as the slicer you use generates commented lines indicating which layer is about to begin, like this line before an example layer number 37: 

; LAYER : 37

Without these lines the G-Code parser will not know which lines correlate to which layers and will not be able to generate a LAYER VIEW of the model. The G-Code can still run, but without seeing a preview of the tool path you can't confirm exactly how the print will be built.